This invention relates generally to electrical stimulation of osteogenesis and specifically to a new method and apparatus for implementing faradic stimulation where electricity is delivered through electrodes.
Electricity is known to stimulate osteogenesis for the treatment of bone disorders although the mechanism by which such stimulation occurs is not precisely known. Three different techniques of electrical stimulation are presently available: faradic, inductive, and capacitive. Of these techniques, faradic stimulation is the oldest historically, the most basic physically, and the most theoretically understood in terms of mechanism. Faradic stimulation involves a net transfer of charge through biological tissue between, typically, an implanted cathode, the negative electrode where osteogenesis occurs, and either an implanted or a topical anode, the positive electrode required only to complete the electrical circuit. A primary electric field, but no magnetic field, is produced at each electrode. Although these exogenous electric fields can alter the endogenous electric fields locally in tissue, the predominant theory offered to explain faradic effects is based on electrochemical reactions that occur at the electrodes. Through these reactions, the products created and the reactants consumed may individually or jointly cause a cellular response. In terms of the actual faradic signal, a constant direct current between cathode and anode is used clinically at present although a constant cathodic potential, the potential between cathode and a reference electrode, is regarded as an improved signal and may find future clinical use.
Prior art systems with a constant direct current signal, described, for example, in U.S. Pat. No. 3,842,841 issued to Brighton et al. on Oct. 22, 1994 and in an article entitled "Present and Future of Electrically Induced Osteogenesis" in Clinical Trends in Orthopaedics, edited by L. R. Straub and P. D. Wilson, Jr., published by Thieme-Stratton, New York, N.Y. 1982, pages 1-15, are designed to maintain a constant current regardless of changes in resistance between cathode and anode. To maintain a constant direct current, the interelectrode potential between cathode and anode as well as the electrodic potentials of the cathode and anode, each with respect to a reference electrode, are permitted to vary. The latter potentials are known generally as electrodic potentials or specifically as cathodic and anodic potentials. Electrochemically, current dictates the rate at which a reaction occurs at an electrode while the electrodic potential dictates the type of reaction and facilitates the relative ease by which that reaction occurs. A constant direct current will, therefore, dictate a constant reaction rate, but the type of reaction and the relative ease by which it occurs can change because the electrodic potential is permitted to vary. Thus, a constant direct current signal believed to be optimal initially may, over the course of chronic use, fall below optimal and become less stimulatory or rise above optimal and become detrimental due, in both cases, to changes in electrodic potential and, subsequently, changes in the type of reaction.
Prior art systems with a constant cathodic potential signal, described, for example, in U.S. Pat. No. 4,519,394 issued to Black et al. on May 28, 1985, which is hereby incorporated by reference, are designed to maintain a constant potential between the cathode and a reference electrode regardless of changes in resistance between cathode and anode. To maintain a constant cathodic potential, the current, the interelectrode potential between cathode and anode, and the anodic potential with respect to the reference electrode are permitted to vary. Electrochemically, as described above, a constant cathodic potential will dictate the type of reaction and the relative ease by which that reaction occurs, but the reaction rate can change because the current is permitted to vary. Thus, a constant cathodic potential signal believed to be optimal initially may, over the course of chronic use, fall below optimal and become less stimulatory due to decreases in current and, subsequently, decreases in the reaction rate. Note, however, that, unlike a constant direct current signal, a constant cathodic potential signal cannot rise above optimal and become detrimental since the cathodic potential is controlled to prevent a change in reaction type. For this reason alone, a constant cathodic potential signal is regarded as an improvement over a constant direct current signal.
Electrochemical reactions, involving electrons which act at the interface between a metal or metallic conduction phase and an electrolyte, occur at electrodes employed in faradic stimulation. As first reported in the article entitled "Electrical Stimulation and Oxygen Tension" by Brighton et al. in Annals of the New York Academy of Sciences, 238, 1974, pages 314-320, hereinafter Brighton et al. (1974), and, in more technical detail, in the article entitled "Cathodic Oxygen Consumption and Electrically Induced Osteogenesis" by Brighton et al. in Clinical Orthopaedics and Related Research, 107, 1975, pages 277-282, hereinafter Brighton et al. (1975), evidence of electrochemical reactions at typical faradic electrodes has been obtained in vitro where consumption of oxygen, elevation of pH, and evolution of hydrogen have all been found to occur at the cathode depending upon the magnitude of the constant direct current. Evidence of electrochemical reactions can also be found from polarization or potentiostatic studies performed with the electrodes either in vitro or in vivo. In a polarization study, a set potential is applied to the cathode (negative) and anode (positive), and then measurements are made of the resultant (a) direct current between cathode and anode, (b) the cathodic potential which is the potential of the cathode with respect to a reference electrode, and (c) the anodic potential which is the potential of the anode with respect to the same reference electrode. In a potentiostatic study, a potential is again applied to the cathode and anode but is permitted to vary in order to result in, by choice, either a set cathodic or anodic potential, and then measurements are made of the resultant (a) direct current between cathode and anode, (b) the interelectrode potential which is the potential applied to the cathode and anode, and (c) either the anodic potential, if a set cathodic potential was chosen, or the cathodic potential, if a set anodic potential was chosen. In either study, the set potential is adjusted over a range from usually zero (0) to less than five (5) volts over time in order to produce a plot of the cathodic and anodic potentials, both with respect to a reference electrode, versus the resulting direct current between cathode and anode, usually with the direct current on logarithmic (log) scale.
An example of a plot from polarization studies performed in vivo with a cathode and anode, both of stainless-steel, in rabbits at implantation sites appropriate for faradic stimulation is presented in FIG. 1, which is extracted from pages 406-407 of "The Mechanism of Faradic Stimulation of Osteogenesis" by Baranowski et al. in Mechanistic Approaches to Interactions of Electric and Electromagnetic Fields With Living Systems, edited by M. Blank and E. Findl, published by Plenum Publishing Corporation, New York, N.Y. 1987, pages 399-416, hereinafter Baranowski et al. (1987), which article is hereby incorporated by reference. Two curves, the result of polynomial regression analyses, are shown for the cathodic and anodic potentials, both with respect to a silver/silver chloride (Ag/AgCl) reference electrode, versus the direct current on log scale. The curves exemplify the relationship between the electrodic potentials and the direct current, essentially the electrochemical behavior of the electrodes, for the specific set of conditions under which the polarization studies were performed.
Of particular interest here is the electrochemical behavior of the cathode since the cathode is the site of osteogenesis in faradic stimulation whereas the anode only serves to complete the circuit. For the cathode, three regions of relatively uniform slope can be distinguished from the curve of cathodic potential versus the direct current shown in FIG. 1. Consecutive regions of uniform slope are joined by a change in slope which takes place at two different locations. The cathodic potential at each of these two slope changes can be determined graphically by superimposing a straight line on each of the three regions of uniform slope until the lines from consecutive regions intersect. When this was performed on the cathodic curve in FIG. 1, the cathodic potentials at the slope changes were found to be -0.59 and -1.26 volt with respect to an Ag/AgCl reference electrode.
In order to identify which reactions occur at an in vivo cathode, the above potentials can be compared to equilibrium potentials of reactions possible in vivo from a potential versus pH diagram. Such a diagram has been developed, as shown in FIG. 2 which is extracted from pages 403-406 of the above-referenced article by Baranowski et al. (1987), from expressions for equilibrium potentials of electrochemical reactions provided in a book by Pourbaix entitled Atlas of Electrochemical Equilibria in Aqueous Solutions, published by Pergamon Press, Oxford, United Kingdom, 1966, hereinafter Pourbaix 1966), for conditions typically found initially at the cathode in vivo and for potentials with respect to an Ag/AgCl reference electrode. Because water, oxygen, hydrogen ions, and hydroxyl ions constitute the predominant chemical species available as reactants in vivo, only reactions involving these reactants as well as hydrogen, hydrogen peroxide, and hydrogen peroxide ion as products from these reactants are considered possible. The dashed vertical line shown in FIG. 2 at an in vivo pH of 7.4 intersects each of the four solid, sloped lines, representing possible reactions, at the potential indicated. A point can be chosen along the vertical line for any particular electrode potential. If the necessary reactants are available, reactions below this chosen point will occur as oxidations at anodes while reactions above the chosen point will occur as reductions at cathodes.
The -0.59 volt potential of the first slope change found in FIG. 1 is comparable to the -0.5211 volt equilibrium potential of the reaction O.sub.2 +2H.sub.2 O+2e.sup.- .revreaction.H.sub.2 O.sub.2 +2OH-- given in FIG. 2 whereas the -1.26 volt potential of the second slope change found in FIG. 1 is comparable to the -1.2031 volt equilibrium potential of the reaction 2H.sub.2 O +2e.sup.- .revreaction.H.sub.2 +2OH-- given in FIG. 2. From this comparison of potentials, a most probable reduction reaction can be related to each of the three regions of uniform slope described for the curve of cathodic potential versus the direct current on log scale.
FIG. 3, which is extracted from pages 407-408 of the above-referenced article by Baranowski et al. (1987), is a generic curve of the cathodic potential versus the direct current on log scale with a reduction process indicated for each of its three regions of relatively uniform slope. This curve depicts the idealized relationships between the cathodic potential and the direct current for a cathode in general and, for this reason, has been drawn with unnumbered axes. However, equilibrium potentials for the reactions determined theoretically from the potential versus pH diagram in FIG. 2 are given in comparison to the potentials of the two slope changes determined experimentally from the in vivo polarization studies presented in FIG. 1.
Referring to FIG. 3, the reduction reaction O.sub.2 +2H.sub.2 O +4e.sup.- .fwdarw.4OH-- occurs in the first region. This oxygen consumption and pH elevation reaction occurs through a single, 4-electron reaction. Two reduction reactions, O.sub.2 +2H.sub.2 O+2e.sup.- .fwdarw.H.sub.2 O.sub.2 +2OH-- plus H.sub.2 O.sub.2 +2e.sup.- .fwdarw.2OH--, occur in the second region, due to the reduction upon production of hydrogen peroxide, to give the overall reaction O.sub.2 +2H.sub.2 O+4e.sup.- .fwdarw.4OH--. This process of intermediate hydrogen peroxide formation, oxygen consumption, and pH elevation occurs through two, 2-electron reactions. The initiation of these two, 2-electron reactions displaces the previous, single, 4-electron reaction which accounts for the first change in slope observed from the curve of the cathodic potential versus the direct current. Finally, the reduction reaction 2H.sub.2 O+2e.sup.- .fwdarw.H.sub.2 +2OH-- occurs in the third region. This hydrogen evolution and pH elevation reaction occurs through a single, 2-electron reaction. The initiation of this single, 2-electron reaction displaces the two, 2-electron reactions which then accounts for the second change in slope.
Under conditions typically found initially in vivo and with respect to an Ag/AgCl reference electrode, the following observations can be made from the analysis of the curve of the cathodic potential versus the direct current and from the comparison of the cathodic potentials at slope changes to the equilibrium potentials of reactions from the potential versus pH diagram. First, a reduction reaction involving oxygen consumption and pH elevation is predicted to occur at a cathode when the cathodic potential is between +0.025 and -0.5211 volt. Second, the same overall reaction is also predicted to occur when the cathodic potential is between -0.5212 and -1.2031 but with the intermediate formation of hydrogen peroxide. Finally, when the cathodic potential is greater than -1.2031 volt, a reduction reaction involving hydrogen evolution and pH elevation is then predicted to occur. Thus, a depressed oxygen tension, an elevated pH, and hydrogen gas formation should be found at an in vivo cathode depending on its potential.
As initially reported in an abstract entitled "Microenvironmental Changes Associated with Electrical Stimulation of Osteogenesis by Direct Current" by Baranowski et al. in Transactions of the Bioelectrical Repair and Growth Society, 2nd Annual Meeting, 1982, page 47 and, in a more detailed publication, in a doctoral dissertation entitled Electrical Stimulation of Osteogenesis by Direct Current: Electrochemically-Mediated Microenvironmental Alterations by Baranowski for the University of Pennsylvania, Philadelphia, Pa., 1983, hereinafter Baranowski (1983), the oxygen tension and pH near a cathode during in vivo faradic stimulation of osteogenesis by constant direct currents were determined and then correlated to the resultant biological response. Depression of oxygen tension and elevation of pH were found to occur at the cathode as a result of reduction processes that are influenced by the cathodic potential of the stimulus. The overall observations strongly indicated that alterations in oxygen tension and pH mediated by the reduction processes at the cathode are actually related to, rather than merely associated with, the biological response elicited by the stimulus. This view is supported by observations that osteogenesis occurs under low oxygen tension and high pH in the absence of electrical stimulation. In fact, many studies have examined the relationship between bone growth and either oxygen tension or pH. The conclusions from these studies are, first, that bone cells follow a predominantly anaerobic metabolic pathway; second, that low oxygen tension and high pH exist at sites of calcification and bone formation; and, third, that high oxygen tension and low pH favors bone resorption rather than formation. Together, the evidence from other studies reinforces the hypothesis that the biological response to faradic stimulation is actually a response to the microenvironmental alterations of oxygen tension and pH mediated by reduction processes at the cathode. This view is in general agreement with early proposed mechanisms of faradic stimulation as presented in the above-referenced articles by Brighton et al. (1974, 1975); in the article entitled "Mechanisms of Stimulation of Osteogenesis by Direct Current" by Black et al. in Electrical Properties of Bone and Cartilage. Experimental Effects and Clinical Applications, edited by C. T. Brighton, J. Black, and S. R. Pollack, published by Grune and Stratton, New York, N.Y. 1979, pages 215-224, hereinafter Black et al. (1979), which is hereby incorporated by reference; and, in more detail, in the above-referenced doctoral dissertation by Baranowski (1983) and in the article entitled "Electrochemical Aspects of D.C. Stimulation of Osteogenesis" by Black et al. in Bioelectrochemistry and Bioenergetics, 12, 1984, pages 323-327.
On the supposition that electrochemically mediated, microenvironmental alterations of oxygen tension and pH elicit the biological response to faradic stimuli, a number of overall conclusions can be made with regard to faradic stimulation.
First, although an anode, or a predominantly positive electrode, is required to complete the circuit in faradic stimulation, it will not be the site of non-traumatic osteogenesis. The potential versus pH diagram shown in FIG. 2 can be employed to predict that oxidation reactions involving oxygen evolution, rather than oxygen consumption, and pH depression, rather than pH elevation, occur at an in vivo anode depending on its potential. Other potential versus pH diagrams, not shown here, would predict that oxidation reactions involving production of chlorine or metallic ions could also occur at this electrode. In addition, intermediate free radicals of oxygen and chlorine may be produced during oxidation reactions involving the evolution of oxygen and chlorine. However, although microenvironmental alterations can be produced at the anode, an elevated oxygen tension and a low pH are conditions appropriate for bone resorption, rather than bone formation, while the presence of chlorine, metallic ions, and free radicals are judged to be cytotoxic if present in sufficient local concentrations. To prevent such reactions and resulting alterations from occurring in vivo during faradic stimulation of osteogenesis, a typical anode is much larger than a cathode in surface area which permits passage of a large current at a very small anodic potential.
Second, although current dictates the rate at which a reduction process occurs at the cathode, the cathodic potential dictates the type of reduction process and facilitates the relative ease by which that reaction occurs. As reported in an abstract entitled "The Role of Cathodic Potential in Electrical Stimulation of Osteogenesis by Direct Current" by Baranowski et al. in Transactions of the Orthopaedic Research Society, 8th Annual Meeting, 1983, page 352, the role of the cathodic potential in faradic stimulation of osteogenesis has been examined by employing cathodes of different metal exposures with a 20 microampere stimulus to obtain cathodes at different potentials but at a fixed, constant direct current. They found that the magnitude of an osteogenic response, free from evidence of necrosis or void spaces which are indicative of hydrogen gas evolution at the cathode, increased directly with cathodic potential over a range from -0.6 to -1.23 volt with respect to Ag/AgCl. From -1.26 to -1.4 volt with respect to Ag/AgCl, the magnitude of the osteogenic response decreased and areas of necrosis and void spaces increased directly with cathodic potential. Based on this and related observations, selection of an appropriate direct current is necessary but not sufficient for faradic stimulation of osteogenesis since, on a proportional basis, differences in cathodic potential produce greater differences in osteogenesis than equivalent differences in current. This has been verified by the finding that equal or greater magnitudes of osteogenesis were elicited by controlled, cathodic potential stimuli between -1.15 and -1.25 volt with respect to Ag/AgCl when compared to a constant direct current of 20 microamperes using identical electrodes, as reported in a abstract entitled "The Cathodic Potential Dose-Response Relationship for Medullary Osteogenesis with Stainless Steel Electrodes" by Dymecki et al. in Transactions of the Bioelectrical Repair and Growth Society, 4th Annual Meeting, 1984, page 29.
Third, since osteogenesis is dependent on the degree of microenvironmental alteration which is then dependent on the rate at which a reduction process occurs at the cathode, the more current delivered at an optimum cathodic potential, the greater the degree of microenvironmental alteration, and, if such alteration is tolerable, the greater the magnitude of osteogenesis.
Lastly, although the generic curve of the cathodic potential versus the direct current on log scale, shown in FIG. 3, was, in part, developed from polarization studies performed with specific, stainless-steel electrodes under conditions typically found initially in vivo and with an Ag/AgCl reference electrode, the three regions of relatively uniform slope and the two slope changes can be identified from polarization or potentiostatic studies performed with electrodes of any design or composition as well as any reference electrode. This is evident in reports entitled "Bioelectrochemical Studies of Implantable Bone Stimulation Electrodes" by Spadaro in Bioelectrochemistry and Bioenergetics, 5, 1978, pages 232-238, hereinafter Spadaro (1978), and "Electrical Osteogenesis--Role of the Electrode Material" by Spadaro in Electrical Properties of Bone and Cartilage. Experimental Effects and Clinical Applications, edited by C. T. Brighton, J. Black, and S. R. Pollack, published by Grune and Stratton, New York, N.Y. 1979, pages 189-192, hereinafter Spadaro (1979), which provide results from potentiostatic studies performed in vitro with electrodes made from cobalt-chrome, gold, platinum, platinum-iridium, silver, tantalum, titanium, as well as stainless-steel with cathodic potentials measured with respect to a saturated, calomel reference electrode. Although not discussed in the above-referenced reports by Spadaro (1978, 1979), each curve exhibits three regions of uniform slope while all curves exhibit two slope changes at two distinct cathodic potentials. Thus, polarization or potentiostatic studies that are performed in vivo with the cathode implanted at the site of desired stimulation and the anode positioned at an appropriate site can be employed to ascertain the initial optimum stimulus for faradic stimulation of osteogenesis. In the first region of the curve of cathodic potential versus the direct current on log scale, substantial osteogenesis is improbable since the microenvironment is not altered significantly by a stimulus in this region. In the third region, osteogenesis occurs but is also accompanied by cellular necrosis, void spaces, and focal coagulation which indicates that a stimulus in this region elicits an osteogenic response either traumatically or with deleterious effects. This form of osteogenic response is generally regarded as reactive bone growth (due to physical and chemical trauma) and not necessarily as bone growth stimulated by the faradic signal which occurs minimally in the first region and maximally in the second region. Finally, optimum faradic stimulation occurs with a stimulus in the second region where osteogenesis occurs in the absence of cellular necrosis, void spaces, or focal coagulation. Within this second region, osteogenesis is increasingly favored as the cathodic potential approaches the transition zone between the second and third regions.
Based upon the last overall conclusion presented above, it would appear that the selection of a faradic stimulus to be used with a particular cathode and anode in specific sites of implantation could be accomplished merely through the performance of a polarization or potentiostatic study which would subsequently permit the identification of an appropriate direct current and cathodic potential near the transition zone between the second and third regions of the resulting curve of the cathodic potential versus the direct current on log scale. However, as first recognized in the above-referenced doctoral dissertation by Baranowski (1983) and then restated in the above-referenced article by Baranowski et al. (1987) on page 412, different types of electrodes, but especially cathodes, to be used in similar implantation sites or even identical electrodes, but again especially cathodes, to be used in different sites would necessitate separate determinations of the stimulus in the manner described above. Furthermore, as later recognized and hereby disclosed by the present inventors, any faradic stimulus based upon initial environmental conditions at the cathode would remain optimal only if such conditions persist over the entire period of faradic stimulation. Thus, a stimulus selected in the above manner would be optimal with a particular cathode and anode in specific implantation sites if, and only if, the period of time necessary to elicit osteogenesis was acute for perhaps no longer than several hours. If, however, the period of stimulation needed to be chronic for more than a day, which is known to be required experimentally in animals and clinically in humans, then the stimulus selected on the basis of a polarization or potentiostatic study performed initially with electrodes surrounded by an unaltered microenvironment would no longer be optimal and may even become detrimental.
Within moments after the initial delivery of a current between cathode and anode, alterations of oxygen tension and pH begin to occur at the cathode due to the reduction reactions involving oxygen consumption plus pH elevation either with or without intermediate hydrogen peroxide formation. These microenvironmental alterations, the same alterations judged to be responsible for stimulation of osteogenesis, result in alterations of the conditions at the cathode surface which affect the electrochemical behavior of the cathode or, essentially, the relationship between the cathodic potential and the direct current. For the curve of cathodic potential versus direct current on log scale, regions of uniform slope and slope changes will still be observed, but the slope of each region and the location of each slope change will change or shift as conditions vary at the cathode surface. This results in a curve that differs over time when compared to one obtained initially with the cathode surrounded by an unaltered microenvironment.
Shifts in the locations of the slope changes due to microenvironmental alterations can be examined by determining how oxygen tension and pH alterations at an in vivo cathode affect the equilibrium potentials. This theoretical examination is possible since the equilibrium and slope change potentials are comparable and, in fact, would be equal if no net current flowed between cathode and anode such that a state of equilibrium prevailed. For the three reactions possible at an in vivo cathode, the theoretical changes in equilibrium or slope change potential due to various alterations in pH and oxygen tension at the cathode surface are as given in Table 1 below. These changes in potential in Table 1 are based on calculations performed with the expressions for the equilibrium potential given in the above-referenced book by Pourbaix (1966) assuming a temperature of 37.degree. C., a pH of 7.4 and an oxygen tension of 50 mm Hg which are all initial conditions typically observed in vivo within medullary canal tissue of long bones. Table 1 was developed by the present inventors and is not considered prior art.
TABLE 1 ______________________________________ Theoretical Changes in Equilibrium or Slope Change Potential Due to pH and Oxygen Tension Alterations at the Cathode Surface Alteration In Alteration Oxygen Oxygen In pH Tension Change In pH Tension from from Equilibrium at at Initial Initial or Cathode Cathode In Vivo In Vivo Slope Change Surface Surface Conditions Conditions Potential (pH Unit) (mm Hg) (pH Unit) (mm Hg) (volt) ______________________________________ 8.4 50 1 0 -0.0615.sup.a,b,c 7.4 25 0 25 -0.0046.sup.a or -0.0092.sup.b 8.4 25 1 25 -0.0661.sup.a or -0.0707.sup.b or -0.0615.sup.c ______________________________________ .sup.a Change in potential for the reaction O.sub.2 + 2H.sub.2 O + 4e.sup.- .revreaction. 4OH .sup.b Change in potential for the reaction O.sub.2 + 2H.sub.2 O + 2e.sup.- .revreaction. H.sub.2 O.sub.2 + .sup.c Change in potential for the reaction 2H.sub.2 O + 2e.sup.- .revreaction. H.sub.2 + 2OH
Referring to Table 1, a pH elevation of one pH unit from a pH of 7.4 to a pH of 8.4, quite probable at the cathode surface, would result in a -0.0615 volt increase in the equilibrium or slope change potentials of all reactions. Like pH, an alteration in oxygen tension can also affect these potentials. A 50 percent depression of oxygen tension from 50 to 25 mm Hg would result in either a -0.0046 or -0.0092 volt increase depending on the reduction reaction. If both a pH elevation of one pH unit and a 50 percent depression of oxygen tension occur, the increase in potential can range from -0.0615 to -0.0707 volt. Overall, significant shifts in the location of the slope changes can be expected as a result of modest alterations of pH and oxygen tension at the cathode surface. However, although the effect of such alterations on equilibrium or slope change potentials can be determined theoretically, the degree to which such alterations occur in vivo cannot be anticipated. Any prediction regarding such alterations from one case to another or even in a single case may be unwarranted since conditions at the cathode may differ initially between cases or at any moment over time. This point is illustrated in FIG. 1 by the scatter of data which was obtained through in vivo polarization studies performed only once, initially, prior to initiation of chronic faradic stimulation, in 13 animal cases bilaterally with identical electrodes in identical implantation sites.
As taught in U.S. Pat. No. 5,056,518 to Pethica et al. on Oct. 15, 1991, tissue impedance and cathode properties may change over time, e.g., with progression of healing. The patent to Pethica et al. identifies a transition or knee of a current-voltage characteristic of an electrode pair used for electrically-induced osteogenesis at which the current increases rather rapidly for small increases in applied voltage. The observation of a large or rapid increase in current for a small increase in potential or voltage signifies that hydrogen gas evolution is occurring at the cathode, as depicted by the third region of the generic curve shown above in FIG. 3. While recognizing the need to adapt for variation in tissue impedance and cathode properties over time, the patent suggests that the operating point should be set beyond the knee of the current-voltage characteristic.
Finally, tissue impedance between cathode and anode, contact impedance at each electrode, and material impedance of each electrode may differ initially between cases and may change over time, as taught, in part, in the above-referenced patent to Pethica et al. These initial differences and temporal changes in various impedances may result in changes and shifts in the curve of cathodic potential versus direct current on log scale. Initial differences and temporal changes in the availability and diffusion of reactants, in particular oxygen, may also occur at each electrode, but especially the cathode, with resulting changes and shifts in the same curve. These differences and changes in the tissue, contact, and material impedances and the availability and diffusion of reactants as well as the initial differences in other environmental conditions between cases and the temporal alterations in microenvironmental conditions at the cathode due to electrochemical reactions as described in detail above, including physical differences in the size, shape, design, composition, and site of implantation or placement of each electrode, among other variables, all influence the electrochemical behavior of the cathode. Therefore, since the electrochemical behavior of the cathode or, more precisely, the existence of electrochemical reactions at the cathode dictates the faradic stimulus to be employed, control of electrochemical reactions would permit optimal faradic stimulation of osteogenesis in each unique case over time.